M/611

As it is well known convergence of lower semibounded closed quadratic forms implies convergence of the associated self-adjoint operators in the norm resolvent sense. We derive a sharp estimate for the rate of convergence. If the sequence $(\mu_n)$ of finite signed Radon measures on $\R$ converges weakly to $\mu$, then the Schr{\``o}dinger operators $-\Delta+ \mu_n$ converge to $-\Delta+ \mu$ in the norm resolvent sense. We sketch a proof and provide an upper bound for the rate of convergence with the aid of the mentioned general result. We give an algorithm for the numerical computation of negative eigenvalues of one-dimensional Schr{\``o}dinger operators $-\Delta + \mu$, $\mu$ a finite signed Radon measure, and use above convergence results in order to derive error bounds. Finally we sketch the three-dimensional analogue. The results have been obtained joined with Robert Fulsche and Katarina Ozanova, respectively.

Johannes Brasche

TU Clausthal